Using tensor network states for multi-particle Brownian ratchets

TL;DR

This paper uses tensor network states to analyze how interactions affect the current in multi-particle Brownian ratchets, revealing a shift in optimal driving frequency with increased particle density.

Contribution

It introduces a tensor network approach to efficiently study many-body effects in flashing ratchets, extending beyond single-particle analysis.

Findings

Maximum current shifts to higher frequencies with increased lattice occupancy.

Tensor network methods accurately reproduce stochastic trajectory sampling.

Interactions significantly influence transport properties in multi-particle ratchets.

Abstract

The study of Brownian ratchets has taught how time-periodic driving supports a time-periodic steady state that generates nonequilibrium transport. When a single particle is transported in one dimension, it is possible to rationalize the current in terms of the potential, but experimental efforts have ventured beyond that single-body case to systems with many interacting carriers. Working with a lattice model of volume-excluding particles in one dimension, we analyze the impact of interactions on a flashing ratchet's current. To surmount the many-body problem, we employ the time-dependent variational principle with a binary tree tensor network, methods discussed at length in a companion paper. Rather than propagating individual trajectories, the tensor network approach propagates a distribution over many-body configurations via a controllable variational approximation. The calculations, which reproduce Gillespie trajectory sampling, identify and explain a shift in the frequency of maximum current to higher driving frequency as the lattice occupancy increases.